Early in the pandemic Australia effectively closed its international border to slow the spread of the coronavirus, with non-citizens banned from visiting except in special circumstances.

Deputy Prime Minister Michael McCormack said Australia was "working with Singapore at the moment potentially for a bubble (beginning) in July".

"As the vaccine rolls out, not only in Australia but in other countries, we will reopen more bubbles," he told public broadcaster ABC.

The Sydney Morning Herald reported the deal would allow Singaporeans and Australians who had been vaccinated to travel between the countries without quarantining.

The newspaper said Canberra is also hoping that people from third countries -- such as international students, business travellers and returning citizens -- could complete two weeks' quarantine in Singapore before flying to Australia.

Singapore has already opened its border to a handful of countries that have controlled the virus, including Australia, and officials have said the city-state would like to establish reciprocal travel corridors.

"If only others start to do it, then we'll have a bubble, you have reciprocity, you can start to travel. And I hope some time this year we can do that," transport minister Ong Ye Kung told local radio Friday.

Australia's 14-day hotel quarantine requirement for arrivals has left tens of thousands of Australians stranded overseas, with caps on returnees introduced as the limited system has been unable to cope with large numbers.

International tourism -- worth about Aus$45 billion (US$35 billion) a year to the country's economy before the pandemic hit -- has evaporated.

Australia already has a one-way "travel bubble" with New Zealand, allowing Kiwis to visit without quarantining, though the scheme has been suspended a number of times in response to virus outbreaks.

Meanwhile, on Sunday Australia recorded its second local case of COVID-19 in as many days after a worker at two hotels used to quarantine people arriving from overseas tested positive for the coronavirus.

The infection is the first locally acquired case of COVID-19 in New South Wales in 55 days. The state's director of population health, Stephen Conaty, said the authorities are testing close contacts of the unnamed worker.

Queensland state, which on Saturday reported Australia's first local infection in two weeks, said on Sunday it has detected no cases in the past 24 hours, Reuters reported.

Saturday's case is a doctor who tested positive after she had treated two patients with the UK variant of the virus. Unsure of the size of the outbreak, Queensland closed hospitals and aged-care facilities to visitors for three days.

Australia has reported just over 29,000 coronavirus infections and 909 COVID-19 deaths, far fewer than many other developed countries, helped by international border closures, lockdowns and strict social-distancing rules.

The federal government said on Sunday it will increase spending on rolling out the national COVID-19 vaccinations by A$1.1 billion ($850 million).